0=x^2-27x-114

Solution for 0=x^2-27x-114 equation:

0=x^2-27x-114

We move all terms to the left:

0-(x^2-27x-114)=0

We add all the numbers together, and all the variables

-(x^2-27x-114)=0

We get rid of parentheses

-x^2+27x+114=0

We add all the numbers together, and all the variables

-1x^2+27x+114=0

a = -1; b = 27; c = +114;
Δ = b2-4ac
Δ = 272-4·(-1)·114
Δ = 1185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{1185}}{2*-1}=\frac{-27-\sqrt{1185}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{1185}}{2*-1}=\frac{-27+\sqrt{1185}}{-2}
$